Hah! I see that you've never been on the customer side of these issues. Try explaining "we can't fix cuz it's not our problem" or "we can't fix cuz our moral compass is just and we shouldn't do things that compromise security over usability"
How about; "It appears our services are blocked by some sort of company firewall or security policy on your end. This is an issue that you should bring up with your IT department. If you can advocate to get them to lift the block against our platform we can offer you XXX"
Guess you haven't worked with any large companies... They're always the ones that cause these kinds of problems, not the small flexible ones. Those large companies are also the ones that will pay the most to solve their problems via external services (both due to number of users and how slow it would be to deal with internally).
"That is managed by X department, we can put in a change request and we'll probably get a timeline for the fix at the beginning of next quarter. We'll re-evaluate if you can help with our issue once they get back to us."
You have to balance it against expecting to receive: "That's funny, because we tried a similar product from Slightly Unjust Moral Compasses, LLC and it worked fine. We'll just switch to them. Goodbye."
Right, and mine likes productivity. I'm sure the business that's expending resources to try and circumvent my firewalls has a firewall and a usage policy that their employees adhere too also.
So if you circumvent my original blocks, as an administrator, I will use my home-field advantage to just start targeting your individual users and remote resources. Suddenly your users can't even get on Google. Then they'll have to come to me for "the talk."
So the decision quickly becomes a) circumvent enough firewalls that you blacklist yourself or b) get all your users blacklisted for using your service.
You're assuming those blocks are there for a reason. But blocking PUT makes no sense. Getting blacklisted here requires a very special mix of incompetence and pettiness that is thankfully rare.
Seems more reasonable than trying circumvent a legitimate restriction. Not every block is an adversary which needs defeating.